Hey I'll trade you for my WRX, it'll fit fine in there 
I used to have a 1996 maxima with a bose system. Each speaker had it's own amplifier with a proprietary connection to the head unit, so there was no way to replace the head unit without also replacing all the speakers (and vice versa). I'm not positive that it is the same for you 370Z, but I wouldn't be surprised. Bose has never been friendly with the aftermarket world. I'll never buy a car with Bose again. Give me a car with a cheap crappy radio and let me replace it myself for less money... anyways, I would try to contact Nissan or Bose and see if you can get the specs for the radio, maybe you'll be able to use the Bose speakers somehow.
As far as mounting it... this thread seems to have covered it (NSFW avatars)
http://my350z.com/forum/370z-audio-and-video/413194-370z-custom-in-dash-stereo-or-not.html
If your radio looks like the third one here, I think the space where the screen is is a double DIN slot. You should be able to mount the pioneer unit there, at least in theory. You'd have to find or make your own brackets though, and all those buttons would become useless. And you'd still have to deal with the wiring.
If you have the second one, I guess your best bet would be to try to track down the parts from the 1st one... probably wouldn't be cheap though. AND you'd still have to deal with the wiring.